3 ms·
It's good. Due to the stiffness of real strings, the overtones do not occur at even multiples of the fundamental frequency. This means that when tuning a pian
by CarVac 5y ago
It's good.
Due to the stiffness of real strings, the overtones do not occur at even multiples of the fundamental frequency.
This means that when tuning a piano, you need to compromise between tuning so that the fundamentals are in tune with distant notes but having the overtones sound discordant with nearby notes, or having sweet overtone matching with nearby notes, causing notes to be very far off when harmonizing at longer distances across the keyboard.
With my upright, I've had more success tuning more based on the fundamental than on the overtones, because it has enough inharmonicity that tuning to the overtones causes right-hand-to-left-hand harmonies to sound noticeably off. But this makes single-hand chords sound messier.
A piano with looooooooooooooooong bass strings can have skinnier strings that are flexible and behave closer to ideal, so you don't have to compromise as much when tuning.
- leephillips 5y agoExcellent explanation. We can get a little quantitative if we remember that the fundamental frequency of a vibrating string is sqrt(T/μ)/(2L), where T is the tension, μ is the linear density, and L is the length. So if we make the string twice as long, (T/μ) has to be increased by a factor of four; if we keep the tension the same we can use a string with 1/4 the linear density, which I guess would decrease the inharmonicity significantly. The square root magnifies the effect of increasing the length, so you get a lot from making the piano a bit longer. The project is a wonderful idea.
- munificent 5y agoFor anyone curious, the name for this tuning technique is "stretch": https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Piano_tuning#Stretch https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning Software synthesized pianos implement this too because it's part of how we expect piano-based instruments to sound.